The Hertz-Type and Adhesive Contact Problems for Depth-Sensing Indentation

Borodich, Feodor M.

doi:10.1016/b978-0-12-800130-1.00003-5

Cited by 121 publications

(98 citation statements)

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“…The progress in development of depth-sensing micro/nanoindentation, see, e.g. reviews by Borodich and Keer [10], Bull [11], Chaudhri and Lim [14] and Borodich [6,7], has made it possible to study various homogeneous materials in small volumes. These techniques were also applied to study mechanical properties of thin films and coated materials, i.e.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of elastic modulus and hardness of highly inhomogeneous materials by nanoindentation

2015

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The experimental and numerical techniques for evaluation of mechanical properties of highly inhomogeneous materials are discussed. The techniques are applied to coal as an example of such a material. Characterization of coals is a very difficult task because they are composed of a number of distinct organic entities called macerals and some amount of inorganic substances along with internal pores and cracks. It is argued that to avoid the influence of the pores and cracks, the samples of the materials have to be prepared as very thin and very smooth sections, and the depth-sensing nanoindentation (DSNI) techniques has to be employed rather than the conventional microindentation. It is shown that the use of the modern nanoindentation techniques integrated with transmitted light microscopy is very effective for evaluation of elastic modulus and hardness of coal macerals. However, because the thin sections are glued to the substrate and the glue thickness is approximately equal to the thickness of the section, the conventional DSNI techniques show the effective properties of the section/substrate system rather than the properties of the material. As the first approximation, it is proposed to describe the sample/substrate system using the classic exponential weight function for the dependence of the equivalent elastic contact modulus on the depth of indentation. This simple approach allows us to extract the contact modulus of the material constitutes from the data measured on a region occupied by a specific component of the material. The proposed approach is demonstrated on application to the experimental data obtained by Berkovich nanoindentation with varying maximum depth of indentation.

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Section: Introductionmentioning

confidence: 99%

Evaluation of elastic modulus and hardness of highly inhomogeneous materials by nanoindentation

2015

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“…Following Borodich [9,10], we introduce a similarity transformation of one solution to the problem into another. We assume that for a value of the contact force F the solution of the contact problem (3.1), (3.2), and (3.4) under the similarity condition (3.16) is given by the contact pressure function p(y), the contact approach quantity δ 0 , and the contact region ω bounded by the contour Γ .…”

Section: Similarity Analysis Of the Contact Problem For Thin Bonded Imentioning

confidence: 99%

Unilateral Frictionless Contact of Thin Bonded Incompressible Elastic Layers

Argatov

Mishuris

2015

Advanced Structured Materials

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This chapter is devoted to solving contact problems for thin bonded incompressible transversely isotropic elastic layers in the thin-layer approximation, based on the leading-order asymptotic model developed in Chap. 2. Asymptotic Model for the Frictionless Contact of Thin Bonded Incompressible LayersIn this section we summarize the results of the asymptotic analysis performed in Sects. 2.5 and 2.7, by formulating a leading-order asymptotic model to describe (in the thin-layer approximation) the frictionless contact interaction of two incompressible elastic layers bonded to rigid substrates. Leading-Order Asymptotic Model for the Unilateral ContactWe will continue use of previous notation, wherever possible, and consider two thin transversally isotropic elastic layers of uniform thicknesses h 1 and h 2 ideally bonded to rigid substrates (see Fig. 3.1). Let ϕ(y) and δ 0 denote the gap between the layer surfaces before deformation and the contact approach of the rigid substrates under the external normal load, respectively.

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“…The force of adhesion for one nano-asperity is assumed as the pull-off force according to Boussinesq-Kendall model, corrected with non-slip coefficient ( ) introduced by Borodich [20,21]. Let Fadh1 be the adhesion force of one asperity and n be the number of asperities in contact.…”

Section: Adhesion Forcementioning

confidence: 99%